In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

‎semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. the model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎stability estimates are obtained for a slightly more general problem.‎ ‎these, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

It is unnecessary, nowadays, to point out the importance of the Schrodinger equation to disciplines of science and technology. In principle, one can understand any natural phenomenon if one can solve the corresponding Schrodinger equations. Unfortunately, the Schrodinger equation can only be analytically solved in a few special cases. Therefore, it is very important to know the properties of th...

S. Prešić ([6]) determined the all reproductive general solutions of the equation r(x) = 1, where r was a unary relation of a given set T . In this paper we determine the all general solutions of this equation. S. Prešić ([6]) introduced the most general concept of equations. Namely, he considered the equation of the form r(x) = 1, where r was a unary relation of a non–empty set S. He gave the ...

 ∂tu = − i ∂xj (ajk(x, t, u, ū,∇u,∇ū)∂xku) +~b1(x, t, u, ū,∇u,∇ū) · ∇u+~b2(x, t, u, ū,∇u,∇ū) · ∇ū + c1(x, t, u, ū)u+ c2(x, t, u, ū)ū+ f(x, t), where x ∈ R, t > 0, and A = (ajk(·))j,k=1,..,n is a real, symmetric matrix. Our aim is to study the existence, uniqueness and regularity of local solutions to the initial value problem (IVP) associated to the equation (1.1). In the case where A = (ajk(·...

In this paper we are concerned with the solutions of the differential equation f ′′′+ ff ′′+g(f ′) = 0 on [0,∞), satisfying the boundary conditions f(0) = α, f ′(0) = β ≥ 0, f ′(∞) = λ, and where g is some given continuous function. This general boundary value problem includes the Falkner-Skan case, and can be applied, for example, to free or mixed convection in porous medium, or flow adjacent ...

The general image quality equation (GIQE) [Leachtenauer et al., Appl. Opt. 36, 8322-8328 (1997)] is an empirical formula for predicting the quality of imagery from a given incoherent optical system in terms of the National Imagery Interpretability Rating Scale (NIIRS). In some scenarios, the two versions of the GIQE (versions 3.0 and 4.0) yield significantly different NIIRS predictions. We comp...

In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). We believe that the fact that this modification is consi...

Equilibria of high-current electron beams in an axial magnetic field are considered at the base of the approach [1] for the two cases of shielded and immersed cathodes. A general wave equation in the electrostatic approximation, which is valid in any selfconsistent equilibrium, was derived under the only assumption of constancy of full particle energy. This equation supplements general steady s...